FROM DARK MATTER TO DEFICIT ANGLES

272 Pages·2014·2.46 MB·English

FROM DARK MATTER TO DEFICIT ANGLES:
EFFECTIVE FIELD THEORY IN COSMOLOGY AND
ADS/CFT
by
Matthew T. Walters
A dissertation submitted to The Johns Hopkins University in conformity with the
requirements for the degree of Doctor of Philosophy.
Baltimore, Maryland
May, 2014
(cid:13)c Matthew T. Walters 2014
All rights reserved
Abstract
The Standard Model (SM) of particle physics, despite its accurate and thoroughly
tested description of nature, is an incomplete theory. Astrophysical observations
indicate an abundance of matter beyond that of the SM, which currently can only be
observed through indirect gravitational effects. The Cosmic Microwave Background
(CMB) provides a means to constrain both the abundance of this dark matter and
the presence of additional light particle species. The SM also fails to provide a
full description of gravity, with many open questions as to the quantum nature of
gravitationalphenomena. Inthisthesis,weconsiderthreedistinctbutcomplementary
means of extending this modern framework.
Conventional attempts to determine the nature of dark matter are insensitive to
models with mass below about a GeV. We consider newly proposed technology which
would allow for the detection of dark matter as light as an MeV in mass, through
the observation of single electron events in semiconductor materials with significantly
lowered thresholds. We find that such detectors would be particularly sensitive to
dark matter with electric and magnetic dipole moments, with a reach many orders of
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ABSTRACT
magnitude beyond current bounds.
We then consider the effects of new light species on the CMB. We perform a thor-
ough survey of natural, minimal models containing new light species and numerically
calculate the precise contribution of each of these models to the CMB. We provide
a map between the parameters of any particular theory and the results of observa-
tional experiments. Using this map, we present new constraints placed by the Planck
experiment on the parameter space of several models containing new light species.
Finally, we study the universal behavior of long-distance gravitational interactions
in AdS from the perspective of conformal field theory (CFT). To do so, we compute
3
the structure of Virasoro conformal blocks in a semi-classical, large central charge
approximation. Using this result, we then prove the existence of large spin operators
with fixed ‘anomalous dimensions’ indicative of the presence of deficit angles in AdS .
3
As we approach the threshold for the BTZ black hole, interpreted as a CFT scaling
2
dimension, the twist spectrum of large spin operators becomes dense. We derive the
BTZ quasi-normal modes and show that primary states above the BTZ threshold
mimic a thermal background for light operators through exchange of the Virasoro
identity block.
Advisor: David E. Kaplan
iii
Acknowledgments
I owe so much to my advisor, Dave Kaplan, whose insight, guidance, and support
have shaped me as a physicist and a person. I am also grateful to Jared Kaplan,
who has taught me a remarkable amount in such a brief period of time. I would
like to thank Chris Brust, Cyrus Faroughy, and George Bruhn for all their help and
patience as officemates. I have also learned a great deal from discussions with many
incredible people, including Ian Anderson, Sean Cantrell, Fabrizio Caola, Liang Dai,
David Ely, Liam Fitzpatrick, Peter Graham, Marc Kamionkowski, Kirill Melnikov,
Reinard Primulando, Surjeet Rajendran, Raman Sundrum, and Junpu Wang. There
are so many others who have helped make the past five years such a great time in my
life, and I will forever be grateful to all of you.
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Dedication
This thesis is dedicated to my parents, Kenneth and Joan Walters. You were my
first teachers and my constant source of love and support. Thank you.
v
Contents
Abstract ii
Acknowledgments iv
List of Tables xi
List of Figures xii
1 Introduction 1
1.1 Light Dark Matter and Direct Detection . . . . . . . . . . . . . . . . 3
1.2 New Light Particles in the Early Universe . . . . . . . . . . . . . . . 4
1.3 AdS/CFT and Long-Distance Interactions . . . . . . . . . . . . . . . 6
2 Semiconductor Probes of Light Dark Matter 9
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Dipole Moments . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 Effective Pointlike Vertex . . . . . . . . . . . . . . . . . . . . 15
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CONTENTS
2.2.3 Broken U(1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Detection Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.1 Basic Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.2 Single Atom Ionization . . . . . . . . . . . . . . . . . . . . . . 18
2.3.3 Semiconductor Valence Band . . . . . . . . . . . . . . . . . . 22
2.3.4 Detection Rate . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4 Sensitivities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.1 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3 New Light Species and the CMB 36
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.1 Relativistic Species and the CMB . . . . . . . . . . . . . . . . 41
Silk Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Early Integrated Sachs-Wolfe Effect . . . . . . . . . . . . . . . 43
3.2.2 Early Universe Thermodynamics . . . . . . . . . . . . . . . . 46
3.2.3 Decoupling, Recoupling, and the Redistribution of Entropy . . 50
3.2.4 Relevant Decoupling Temperatures . . . . . . . . . . . . . . . 54
3.2.5 Big Bang Nucleosynthesis . . . . . . . . . . . . . . . . . . . . 57
3.2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
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CONTENTS
3.3 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3.1 Spin-0: Goldstone Boson . . . . . . . . . . . . . . . . . . . . . 63
3.3.2 Spin-1: Light Fermion . . . . . . . . . . . . . . . . . . . . . . 74
2
Gauge Interactions . . . . . . . . . . . . . . . . . . . . . . . . 74
Dipole and Anapole Moments . . . . . . . . . . . . . . . . . . 75
Four-Fermion Interactions . . . . . . . . . . . . . . . . . . . . 78
3.3.3 Spin-1: Gauge Boson . . . . . . . . . . . . . . . . . . . . . . . 82
Kinetic Mixing and Gauge Interactions . . . . . . . . . . . . . 83
Dipole Moments . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.3.4 Spin-3: Gravitino . . . . . . . . . . . . . . . . . . . . . . . . . 92
2
3.3.5 Spin-2: Graviton . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.3.6 Models with Light Masses . . . . . . . . . . . . . . . . . . . . 94
3.3.7 Models without New Light Species . . . . . . . . . . . . . . . 98
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4 Universality of Long-Distance AdS Physics from CFT Bootstrap 105
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.2 Defining Long-Distance AdS Physics in CFT Terms . . . . . . . . . . 118
4.2.1 AdS : the Newtonian Gravitational Potential . . . . . . . . 127
≥4
4.2.2 Deficit Angles in AdS from Sub-Planckian Objects . . . . . . 131
3
4.2.3 Quasi-Normal Mode Spectrum from Super-Planckian Objects 133
4.3 Review of the Bootstrap Derivation for d ≥ 3 . . . . . . . . . . . . . . 136
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CONTENTS
4.3.1 Bootstrap Recap . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.3.2 The Bootstrap in Generalized Free Theories . . . . . . . . . . 140
4.3.3 Lightcone OPE Limit and Cluster Decomposition . . . . . . . 143
4.3.4 Anomalous Dimensions and Long-Range Forces in AdS . . . . 146
4.4 Virasoro Blocks and the Lightcone OPE Limit . . . . . . . . . . . . . 151
4.4.1 AdS Deficit Angles from Semi-Classical Virasoro Blocks . . . 153
3
4.4.2 BTZ Quasi-Normal Modes from Semi-Classical Virasoro Blocks 158
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
A Ionization of Atoms by Dark Matter 165
B Details of Boltzmann Equation Code 170
C Properties of Global Conformal Blocks 178
C.1 Factorization at Large (cid:96) and Small u . . . . . . . . . . . . . . . . . . 179
C.2 Further Approximations at Small u . . . . . . . . . . . . . . . . . . . 180
C.3 Global Conformal Blocks in the Heavy/Light Probe Limit . . . . . . 181
D Direct Approach to Virasoro Conformal Blocks 183
D.1 Virasoro Blocks and Projection Operators . . . . . . . . . . . . . . . 184
D.2 Semi-Classical Graviton Basis . . . . . . . . . . . . . . . . . . . . . . 186
D.3 T Correlators and the Identity Virasoro Block . . . . . . . . . . . . 189
µν
E Review of Monodromy Method for the Virasoro Blocks 193
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CONTENTS
E.1 Scaling of the Semi-Classical Action . . . . . . . . . . . . . . . . . . . 195
E.2 Insertion of the Degenerate Operator . . . . . . . . . . . . . . . . . . 197
E.3 Differential Equation from the Degeneracy Condition . . . . . . . . . 199
E.4 Constraint on h and Monodromy . . . . . . . . . . . . . . . . . . . . 201
β
F Computing Virasoro Blocks via the Monodromy Method 203
F.1 S-Channel Virasoro Blocks . . . . . . . . . . . . . . . . . . . . . . . . 204
F.2 S-Channel Virasoro Blocks at Quadratic Order . . . . . . . . . . . . . 209
G T-Channel Virasoro Blocks 211
H Calculation of Deficit Angle Spectrum 215
H.1 Bootstrap Equation in the Lightcone OPE Limit . . . . . . . . . . . . 215
H.2 Bounds on Coefficient Density . . . . . . . . . . . . . . . . . . . . . . 220
Bibliography 224
Vita 260
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